Consider these
There is an apple, an orange and a banana on the table.
There are an apple, an orange and a banana on the table.
which one should I use?
If you reorder the sentence, you will see the answer:
An apple, and orange, and a banana are on the table.
So, you should say
There are an apple, an orange and a banana on the table.
The number of "there is/are" should agree with the grammatical number of the subject, which is the series, and it is taken as plural, though its elements are all singular.
Sometimes "there's", a contraction of "there is", is used in informal contexts even with a plural subject. See this link for more information:
"There are" sounds bad when it's followed by a list of items. It is often better to use the singular verb 'is' in a construction like this :
There is a kitchen, a living room, and a bedroom in my apartment.
Source : https://www.grammarly.com/blog/there-is-there-are/
As you are mentioning a list of items, each beginning with the indefinite article 'a'/'an' you may write :
There is an apple, an orange and a banana on the table.
But to avoid the confusion, it's better to rewrite the sentence like this :
An apple, an orange and an banana are on the table.